基于主动学习Kriging模型的可靠性分析

Reliability Analysis Based on Active Learning Kriging Model

论文采用Kriging模型代替结构真实功能函数,引入主动学习函数,序列选择最佳样本点,在每次迭代中加入最佳样本点更新Kriging模型.与直接的蒙特卡洛方法相比,主动学习Kriging模型仅需要少量的结构分析就能够得到精度较高的可靠度结果,适用于实际工程具有隐式功能函数的结构可靠性分析.论文通过三个数学算例,从最佳样本点的分布情况、功能函数的拟合程度及可靠度计算结果出发对四种学习函数进行对比研究,最后对具有隐式功能函数的悬臂板进行可靠度分析.结果表明,主动学习函数的引入,合理选择了Kriging模型所需的样本,提高了计算效率,同时,学习函数的选择对结构可靠性分析结果也存在影响.

In practical engineering,structural reliability analysis is usually characterized with implicit performance functions and time-consuming structural responses.It is not efficient to utilize Monte Carlo simulation that requires a large number of samples.Aiming at this issue,the original structural performance function is approximated using the Kriging model.However,to obtain an accurate Kriging model with a large number of samples,the computation cost is increased.Therefore,the active learning method is utilized to sequentially select a best next point to update the original Kriging model progressively.An accurate reliability result can be obtained with few sample points in comparison with the direct Monte Carlo simulation,indicating apotential of the proposed method for reliability analysis with implicit performance function.Four different learning functions are introduced in this paper,and the corresponding distribution of the best next points,the approximation of performance functions and the accuracy of reliability results are compared through three numerical examples.And finally,reliability analysis for a cantilever plate with an implicit performance function is carried out.The results demonstrate that the computation efficiency is improved by utilizing the Kriging model combined with active learning methods.The accuracy of reliability result is found to be affected by the choice of active learning functions.